Hello all!
I would really appreciate some help.
Mathematica has a built-in function called Series:
Series[x,x_0,n],
which allows to expand functions into power series where x is the
variable, x_0 is the point about which we expand, and n is the desired
order of expansion.
It also allows x_0 to be infinity, which is very useful when one needs
multiple expansion (as in gravitational waves and electromagnetic
radiation).
Although is allows to expand series in terms of 1/x and writes O(1/x)
(and its powers) in the output, it does not allow this to be entered in
the input. To convince yourselves, try it out. Enter in the input,
e.g., 1+ 1/r+ (O(1/r))^2, and it will tell you that 1/r is not a
variable.
If, on the other hand, you entered:
In=Series[1/(r+1), {r, Infinity,3}]//Simplify
you will get
Out=1/r-(1/r)^2+(1/r)^3+(O(1/r))^4
which shows that the output is possible, but the input is impossible.
Can anyone offer some assistance?
Thanks,
Gideon